Problem: Simplify the following expression: $ n = \dfrac{1}{5} - \dfrac{7}{k + 4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k + 4}{k + 4}$ $ \dfrac{1}{5} \times \dfrac{k + 4}{k + 4} = \dfrac{k + 4}{5k + 20} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{7}{k + 4} \times \dfrac{5}{5} = \dfrac{35}{5k + 20} $ Therefore $ n = \dfrac{k + 4}{5k + 20} - \dfrac{35}{5k + 20} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{k + 4 - 35 }{5k + 20} $ Distribute the negative sign: $n = \dfrac{k + 4 - 35}{5k + 20}$ $n = \dfrac{k - 31}{5k + 20}$